Demographic gravitation is a concept of "social physics", introduced by Princeton University astrophysicist John Quincy Stewart in 1947. It is an attempt to use equations and notions of classical physics - such as gravity - to seek simplified insights and even laws of demographic behaviour for large numbers of human beings. A basic conception within it is that large numbers of people, in a city for example, actually behave as an attractive force for other people to migrate there, hence the notion of demographic gravitation. It has been related to W. J. Reilly's law of retail gravitation, George Kingsley Zipf's Demographic Energy, and to the theory of Trip distribution through gravity models Trip distribution#Gravity model.
Writing in the journal Sociometry, Stewart set out an "agenda for social physics." Comparing the microscopic versus macroscopic viewpoints in the methodology of formulating physical laws, he made an analogy with the social sciences:
Fortunately for physics, the macroscopic approach was the commonsense one, and the early investigators - Boyle, Charles, Gay-Lussac - were able to establish the laws of gases. The situation with respect to "social physics" is reversed... If Robert Boyle had taken the attitude of many social scientists, he would not have been willing to measure the pressure and volume of a sample of air until an encyclopedic history of its molecules had been compiled. Boyle did not even know that air contained argon and helium but he found a very important law.
Stewart proceeded to apply Newtonian formulae of gravitation to that of "the average interrelations of people" on a wide geographic scale, elucidating such notions as "the demographic force of attraction," demographic energy, force, potential and gradient.
The following are some of the key equations (with plain English paraphrases) from his article in sociometry:
(Demographic Force = (population 1 multiplied by population 2) divided by (distance squared))
(Demographic Energy = (population 1, multiplied by population 2) divided by distance; this is also Zipf's determinant)
(Demographic Potential of population at point 1 = population at point 2, divided by distance)
(Demographic Potential in general = population divided by distance, in persons per mile)
(Demographic Gradient = persons per (i.e. divided by) square mile)
For comparison, Reilly's retail gravity equilibrium (or Balance/Break Point) is paraphrased as:
(Population 1 divided by (distance to balance, squared) = Population 2 / (distance to balance, squared))
- Reilly's law of retail gravitation
- Trip distribution: Gravity Model
- George Kingsley Zipf's Demographic Energy
- Central place theory
- Johann Heinrich von Thünen's spatial economics
- Walther Christaller's central place theory
- Alfred Weber's least cost location theory.
- Economic rent: Land rent.
- John Quincy Stewart, 1947. Empirical Mathematical Rules Concerning the Distribution and Equilibrium of Population, Geographical Review, Vol 37, 461–486.
- John Quincy Stewart, 1950. Potential of Population and its Relationship to Marketing. In: Theory in Marketing, R. Cox and W. Alderson (Eds) ( Richard D. Irwin, Inc., Homewood, Illinois).
- Zipf, G. K., 1946. The P1 P2/D Hypothesis: On the Intercity Movement of Persons. American Sociological Review, vol. 11, Oct
- Zipf, G. K., 1949. Human Behaviour and the Principle of Least Effort. Massachusetts
- Stewart, J.Q. "The Development of Social Physics", American Journal of Physics, Vol 18 (1950), pp. 239-253
- Vecchia, Karla J., John Q. Stewart Papers (C0571)1907-1970s A Finding Aid, Manuscripts Division Department of Rare Books and Special Collections, Princeton University Library, 2004 
- Stewart, John Q., "Demographic Gravitation: Evidence and Applications," Sociometry, Vol. 11, No. 1/2. (February - May 1948), pp. 31-58. JSTOR 2785468
- Reiser, Oliver L. "Technology and Society" in Kostelanetz, Richard (Ed.), Beyond Left and Right: Radical Thought for Our Times p. 85, William Morrow & Co., New York, 1968. 
- Higgins, Benjamin, and Savoie, David J. "Regional development theories and their application", pp.151-155, Transaction Publishers, New Jersey, 1997. 
- Reilly, W.J. “Methods for the Study of Retail Relationships” University of Texas, Bulletin No 2944, November 1929.
- Reilly, W.J. "The Law of Retail Gravitation", New York, 1931.
- Stewart, J.Q. “Demographic Gravitation: Evidence and Application” Sociometry, Vol. XI, February–May 1948, pp 31-58.